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5. Spectral Analysis

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Table of Contents

• 5.1 | Load the preprocessed spectrum

• 5.2 | Give the line centers, intensity, and width to the module and fit the lines

  • 5.2.1 | Select wavelength range

  • 5.2.2 | Initialize class

  • 5.2.3 | Fit Spectrum and visualize, EDA the spectroscopic parameters

• 5.3 | Save output

# Import necessary modules
from Xpectra.SpecFitAnalyzer import SpecFitAnalyzer
from Xpectra.LineAssigner import *
from Xpectra.SpecStatVisualizer import plot_fitted_als_bokeh, plot_spectra_errorbar_bokeh

5.1 - Load the processed spectra and the line centers

\(\rightarrow\) In the previous step, we located the peaks in the methane laboratory spectrum. Let’s load them, as well as the spectrum itself:

# Call environment variable and assign path to data
__reference_data_path__ = os.getenv("Xpectra_reference_data")

# Import baseline corrected spectrum
corrected_spectrum = pd.read_csv(os.path.join(__reference_data_path__,'processed_data','arpls_baseline_corrected_methane_spectrum.csv'))

# Assign wavenumber (x) and signal (y) arrays
x = corrected_spectrum['original_x'].dropna().to_numpy()
y = corrected_spectrum['original_y'].dropna().to_numpy()

x_baseline_corr = corrected_spectrum['baseline_corrected_x'].dropna().to_numpy()
y_baseline_corr = corrected_spectrum['baseline_corrected_y'].dropna().to_numpy()

corrected_spectrum.head()

	original_x	original_y	cleaned_x	cleaned_y	baseline_corrected_x	baseline_corrected_y
0	2898.543060	0.643845	2898.543060	0.440297	2898.543060	0.014491
1	2898.543908	0.646336	2898.543908	0.436436	2898.543908	0.017204
2	2898.544766	0.645778	2898.544766	0.437300	2898.544766	0.016869
3	2898.545133	0.639101	2898.545133	0.447693	2898.545133	0.010415
4	2898.545638	0.630384	2898.545638	0.461426	2898.545638	0.001921

# Import spectral lines
spectral_lines = pd.read_csv(os.path.join(__reference_data_path__,'processed_data',"closest_hitran_lines_auto.csv"))

# Define arrays
peak_locations = spectral_lines["peak_center"].to_numpy()
peak_heights = spectral_lines["peak_heights"].to_numpy()

\(\rightarrow\) Visualize the imported spectra:

# Obtain previously fitted baseline by reverse correcting the spectrum
spectral_baseline = y - y_baseline_corr

plot_fitted_als_bokeh(wavenumber_values = x,
                      signal_values = y,
                      fitted_baseline = spectral_baseline,
                      baseline_type = 'arpls'
                     )

Loading BokehJS ...

\(\rightarrow\) Create initial guesses array of Gaussian peak parameters

# Initial guesses need {center, height, width}
num_peaks = len(peak_locations)

# Obtain arrays shape (1, num_peaks)
width_guesses = np.array([np.ones(num_peaks)]).T * 0.001
peak_guesses = np.array([peak_locations]).T
height_guesses = np.array([peak_heights]).T

# Initial guesses: shape (3, num_peaks)
initial_guesses = np.hstack((peak_guesses, height_guesses, width_guesses))

5.2 - Fit the spectral peaks

Xpectra.SpecFitAnalyzer module has 3 essential purposes: process spectral data (completed), fit and correct spectral baseline (completed), and identify and fit spectral peaks (current).

At this step, we use line profile functions to model the shape of the spectral peaks and extract spectroscopic parameters.

5.2.1 - Select wavelength range for analysis

wavenumber_range = (2911.15, 2911.9) # cm^-1

plot_spectra_errorbar_bokeh(wavenumber_values = x_baseline_corr,
                            signal_values = y_baseline_corr,
                            wavenumber_range = wavenumber_range,
                            absorber_name = 'CH4',
                            plot_type = 'line')

Loading BokehJS ...

5.2.2 - Initialize class

\(\rightarrow\) Using SpecFitAnalyzer, input baseline-corrected spectrum, absorber name, and environment variable

# Initialize SpecFitAnalyzer
specfit = SpecFitAnalyzer(wavenumber_values = x_baseline_corr,
                          y_baseline_corrected = y_baseline_corr,
                          absorber_name = 'CH4',
                          __reference_data__ = __reference_data_path__)

5.2.3 - Fit Spectrum and Visualize

\(\rightarrow\) Here are the line profile options:

• Gaussian(x) = amplitude * np.exp(-(x - center) ** 2 / (2 * width ** 2))

• Lorentzian(x) = amplitude / (1 + ((x - center) / width) ** 2)

• Voigt(x) = amplitude * np.real(wofz(z)).astype(float) / (sigma * np.sqrt(2 * np.pi))

  • sigma = wid_g / np.sqrt(2 * np.log(2))

  • gamma = wid_l / 2

  • z = ((x - center) + 1j * gamma) / (sigma * np.sqrt(2))

\(\rightarrow\) Fit spectral lines with Gaussian line profile

specfit.fit_spectrum(initial_guesses,
                     line_profile = 'gaussian', # Default
                     wavenumber_range = wavenumber_range,
                     __plot_bokeh__ = True,
                     __print__ = True, # Display fitted params and error bars
                    )

Loading BokehJS ...

	Peak Number	Center	Center Error	Intensity	Intensity Error	Width	Width Error
0	1	2911.6974	0.0012	0.214	0.0566	0.004	0.0012
1	2	2911.6764	0.0025	0.104	0.0543	0.004	0.0025
2	3	2911.6230	0.0004	0.576	0.0468	0.005	0.0004
3	4	2911.5187	0.0016	0.169	0.0544	0.004	0.0016
4	5	2911.4009	0.0005	0.475	0.0491	0.004	0.0005
5	6	2911.3481	0.0004	0.579	0.0442	0.005	0.0005
6	7	2911.2862	0.0006	0.432	0.0508	0.005	0.0006
7	8	2911.2618	0.0004	0.609	0.0403	0.006	0.0004
8	9	2911.1865	0.0005	0.537	0.0492	0.004	0.0005

\(\rightarrow\) EDA on fitted parameters, compare initial guesses to the fitted:

# Convert lists to arrays
guess_arr = np.array(initial_guesses)
fit_arr = specfit.fitted_params

# Create DataFrame with fitted vs. guessed params
df = pd.DataFrame({
    'center_guess': guess_arr[:,0],
    'center_fit': fit_arr[:,0],
    'intensity_guess': guess_arr[:,1],
    'intensity_fit': fit_arr[:,1],
    'width_guess': guess_arr[:,2],
    'width_fit': fit_arr[:,2]})
display(df)

	center_guess	center_fit	intensity_guess	intensity_fit	width_guess	width_fit
0	2911.697485	2911.697411	0.210332	0.213843	0.001	0.004055
1	2911.676406	2911.676367	0.106295	0.103791	0.001	0.004023
2	2911.623123	2911.623013	0.571206	0.575718	0.001	0.004631
3	2911.518359	2911.518673	0.168570	0.168550	0.001	0.004378
4	2911.400698	2911.400869	0.471979	0.475202	0.001	0.004427
5	2911.348160	2911.348104	0.572617	0.579227	0.001	0.005059
6	2911.286321	2911.286236	0.439682	0.432089	0.001	0.004633
7	2911.261846	2911.261797	0.608428	0.609348	0.001	0.005632
8	2911.186087	2911.186549	0.524801	0.536988	0.001	0.004440

5.3 - Save the results: Plots, dfs

\(\rightarrow\) Plot with Seaborn and save as a PDF

specfit.fit_spectrum(initial_guesses,
                     line_profile = 'gaussian', # Default
                     wavenumber_range = wavenumber_range,
                     __plot_seaborn__ = True,
                     __save_plots__ = True, # Display guesses and fitted params
                     __show_plots__ = False
                    )

<Figure size 7000x4200 with 0 Axes>

\(\rightarrow\) Save fitted parameters in a CSV file

df = pd.DataFrame(specfit.fitted_params, columns = ['center','height','width'])

display(df)

	center	height	width
0	2911.697411	0.213843	0.004055
1	2911.676367	0.103791	0.004023
2	2911.623013	0.575718	0.004631
3	2911.518673	0.168550	0.004378
4	2911.400869	0.475202	0.004427
5	2911.348104	0.579227	0.005059
6	2911.286236	0.432089	0.004633
7	2911.261797	0.609348	0.005632
8	2911.186549	0.536988	0.004440

# Define file name
file_name = "fitted_gaussian_lines.csv"

# Save DataFrame to CSV
df.to_csv(os.path.join(__reference_data_path__,'processed_data',file_name), index=False)